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Difficulty: MediumMonopoly: Characteristics and Sources of Monopoly Power

Which of the following revenue relationships is a defining characteristic of a pure monopolist?

  1. Marginal revenue is less than average revenue at all positive levels of outputAnswer
  2. B
    Marginal revenue is equal to price and average revenue at all output levels
  3. C
    Average revenue slopes upward as total output increases due to market power
  4. D
    Total revenue continues to rise indefinitely as price is increased

Answer

Marginal revenue is less than average revenue at all positive levels of output.
A monopolist faces the downward-sloping market demand curve. Since average revenue equals price (AR=PAR = P), reducing price to increase sales causes marginal revenue (MRMR) to fall twice as fast as average revenue, making MR<ARMR < AR for all positive output levels.

Step-by-Step Solution

1
Analyze the demand curve faced by a monopolist
The monopolist is the sole supplier in the industry, so its demand curve is the downward-sloping market demand curve (P=ARP = AR).
Since the firm is a price maker, selling additional units requires reducing the price on all previous units.
2
Derive the relationship between Average Revenue (AR) and Marginal Revenue (MR)
Because price must be lowered on all units to sell one additional unit, the additional revenue gained from the last unit (MRMR) is less than the price (ARAR) of that unit.
Mathematical relationship: MR=P+Q⋅dPdQMR = P + Q \cdot \frac{dP}{dQ}, where dPdQ<0\frac{dP}{dQ} < 0, ensuring MR<ARMR < AR for all Q>0Q > 0.

Key Concept

Revenue Characteristics of Monopoly
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Topics

Monopoly: Characteristics and Sources of Monopoly Power

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